What is the mole?

The mole is the SI base unit that measures amount of substance. The symbol for amount of substance is n. By definition, the mole contains a defined number of entities (usually atoms or molecules). This number is called 'the Avogadro constant' (N_A). The mole is used to describe a practical quantity of material. It is the link between the microscopic and macroscopic worlds and is used to scale phenomena from the atomic up to 'relevant' sizes.

How big is a mole?

A mole is the amount of substance containing as many elementary entities as there are atoms in exactly 0.012 kilogram (or 12 grams) of carbon-12, where the carbon-12 atoms are unbound, at rest and in their ground state

The current value for N_A is 6.022 141 79(30)x10²³ mol^-1 (2007 CODATA).

This number is a dauntingly large figure.

• This number of sand grains would cover the United Kingdom to a depth of about 40 centimetres.
• There are about this number of human cells on Earth.
• This number of grapefruit would have approximately the same volume as the Earth.
• It would take you twenty thousand million million years to count this number of coins (counting about one coin per second).

The mole in use (and implications of knowing it more accurately)

In reality, chemists rarely measure amount of substance directly. Most chemical measurements require the determination of the composition of mixtures, rather than an absolute determination of the amount of substance present (e.g. the concentration of lead in drinking water). In practical usage, amount of substance is usually combined with other (extensive) quantities such as volume or mass to derive quantities that measure the composition of mixtures such as concentration. These quantities are intensive because their magnitude is the same for all parts of the system they describe.

According to the present definition of the mole, our knowledge of the amount of substance present relies on our knowledge of the relative molecular mass of the substance being analysed and its mass within the sample. Currently, therefore, amount of substance is strongly linked to the measurement of mass. Chemists also use the mole when describing the stoichiometry (or balancing) of reactions. In combining hydrogen and oxygen to make water in the reaction:

2H₂ + O₂ = 2H₂O

Two moles of hydrogen react with one mole of oxygen to yield two moles of water.

As chemical reactions take place at atomic scales, the mole is invaluable in representing equations describing these reactions with respect to practicable mass scales.

The story of the mole

1808: The English scientist John Dalton developed his 'atomic theory' that elements are made up of atoms.

1902: Wilhelm Ostwald introduced the concept of the 'mole' or gram-molecule. Written in its original German as Mol, a shortened version of Molekül (German for molecule).

1959: The mole was defined by IUPAP and IUPAC as the number of atoms of oxygen comprising a mass of 16 g. Physicists refined this definition to involve the oxygen-16 isotope only.

1959/1960: The mole was redefined in terms of carbon-12 as the amount of substance of a system which contains as many elementary entities as there are atoms in exactly 0.012 kilogram of carbon-12; its symbol is mol.

1971: Mole adopted by the 14th GCPM (General Conference on Weights and Measures).

1980: The CIPM refined the definition, stating that the carbon-12 atoms are unbound and in their ground state.

Is the mole dimensionless?

Curiously perhaps, the mole is not dimensionless, as it is the unit for 'amount of substance'. It is a unit, not just a scaling factor.

The requirement to use amount of substance to form intensive quantities illustrates one of the principal reasons why the mole was adopted as a base unit of the SI. It is necessary to include the mole as a part of the SI in order to highlight that it refers to an extensive quantity, which can be combined into a ratio with another extensive quantity (e.g. mass, volume) to form an intensive quantity (e.g. concentration).

Present work, and the future for the mole

The mole is not realised as a unique physical artefact like the prototype kilogram held at BIPM. However, it can be realised by certain reproducible experimental methods known as 'primary methods'. One example is by weighing a sample of material of known composition.

In common with several other SI units, the definition of the mole is presently being reconsidered. Since it is related to the kilogram, there is a pressure to reconsider its definition and relate it more directly to a specified number of entities. This would lead to a fixed value for 'the Avogadro constant'.

Scale of mol

To create these data, we found the mean atomic mass that equates to the mass of one mole in grams:

Approximate mass of one mole of this substance	Substance
0.002 kg	Hydrogen gas (H2)
0.018 kg	Water
0.196 kg	Gold
0.342 kg	Table sugar (C12H22O11)
66 kg	Haemoglobin molecule
995 kg	DNA molecule
3 000 kg	Ultra high molecular weight polyethylene

The mass of DNA, proteins and other organic molecules is usually expressed in daltons. A dalton, also known as an atomic mass unit, is roughly the mass of a single proton or neutron. In relation to the SI mass unit, a dalton is about 1.7 yoctograms.